Finite time singularities for the free boundary incompressible euler equations

By Angel Castro; Diego Córdoba; Charles Fefferman; Francisco Gancedo; Javier Gómez-Serrano

doi:10.4007/annals.2013.178.3.6

Finite time singularities for the free boundary incompressible euler equations

By Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, Javier Gómez-Serrano

Mathematics

Research output: Contribution to journal › Article › peer-review

81 Scopus citations

Abstract

In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem) for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity.

Original language	English (US)
Pages (from-to)	1061-1134
Number of pages	74
Journal	Annals of Mathematics
Volume	178
Issue number	3
DOIs	https://doi.org/10.4007/annals.2013.178.3.6
State	Published - 2013

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.4007/annals.2013.178.3.6

Cite this

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abstract = "In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem) for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity.",

author = "Castro, {By Angel} and Diego C{\'o}rdoba and Charles Fefferman and Francisco Gancedo and Javier G{\'o}mez-Serrano",

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AU - Córdoba, Diego

AU - Fefferman, Charles

AU - Gancedo, Francisco

AU - Gómez-Serrano, Javier

PY - 2013

Y1 - 2013

N2 - In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem) for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity.

AB - In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem) for which the smoothness of the interface breaks down in finite time into a splash singularity or a splat singularity.

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M3 - Article

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SN - 0003-486X

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EP - 1134

JO - Annals of Mathematics

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Finite time singularities for the free boundary incompressible euler equations

Abstract

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